||The conventional approach for steady state solution of partial differential equation is Newton-Raphson method. However, the computational cost of Newton-Raphson's method is high. Moreover, convergence is not gauranteed unless the initial guess is sufficiently close to the exact solution. Recently, the method of time marching is also used for solving steady-state problem. The time marching method is easy to analyze and implement on computer but its convergence speed is usually slow. In this thesis, the time marching method and associated techniques to speed up the convergence are studied. Specifically, the third stage Runge-Kutta method for hyperbolic and parabolic equation will be discussed. Some results about the parameters of Runge-Kutta method and time marching method will be presented .